On Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems

Dennis Cheung (50003110student.cityu.edu.hk)
Felipe Cucker (macuckermath.cityu.edu.hk)
Raphael Hauser (hausercomlab.ox.ac.uk)

Abstract: In this paper we study the distribution tails and the moments of a condition number which arises in the study of homogeneous systems of linear inequalities. We consider the case where this system is defined by a Gaussian random matrix and characterise the exact decay rates of the distribution tails, improve the existing moment estimates, and prove various limit theorems for large scale systems. Our results are of complexity theoretic interest, because interior-point methods and relaxation methods for the solution of systems of linear inequalities have running times that are bounded in terms of the logarithm and the square of the condition number respectively.

Keywords: condition number, random matrices, linear programming, probabilistic analysis, complexity theory

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: NA-03/08, Oxford University Computing Laboratory, Wolfson Bulding, Parks Road, Oxford, OX1 3QD. September 2003

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Entry Submitted: 09/17/2003
Entry Accepted: 09/17/2003
Entry Last Modified: 09/17/2003

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